A multi-region discrete-time mathematical modeling and optimal control of an electoral behavior

Abstract

We study in this work, a discrete mathematical model that describes the dynamics of citizens who have the right to vote and their electoral behavior with regard to a political party during an awareness program in many regions whose individuals have a mutual influence. Also, we propose an optimal strategy for an awareness program or an election campaign that helps politicians to distinguish between different regions and categories of voters in order to increase the registered rate in the electoral process in many regions and obtain the greatest possible number of votes with a minimal effort. Pontryagin’s maximum principle, in discrete time, is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical simulation is carried out using Matlab. Consequently, the obtained results confirm the performance of the optimization strategy.